SIAM Journal on Optimization最新文献

Corrigendum and Addendum: Newton Differentiability of Convex Functions in Normed Spaces and of a Class of Operators 更正和增补：规范空间中凸函数和一类算子的牛顿可微性

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-16 DOI: 10.1137/24m1669542

Martin Brokate, Michael Ulbrich

引用次数: 0

Newton-Based Alternating Methods for the Ground State of a Class of Multicomponent Bose–Einstein Condensates 基于牛顿的一类多组分玻色-爱因斯坦凝聚态基态交替法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-11 DOI: 10.1137/23m1580346

Pengfei Huang, Qingzhi Yang

引用次数: 0

Minimum Spanning Trees in Infinite Graphs: Theory and Algorithms 无限图中的最小生成树：理论与算法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-11 DOI: 10.1137/23m157627x

Christopher T. Ryan, Robert L. Smith, Marina A. Epelman

引用次数: 0

A Functional Model Method for Nonconvex Nonsmooth Conditional Stochastic Optimization 非凸非光滑条件随机优化的函数模型方法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-10 DOI: 10.1137/23m1617965

Andrzej Ruszczyński, Shangzhe Yang

{"title":"A Functional Model Method for Nonconvex Nonsmooth Conditional Stochastic Optimization","authors":"Andrzej Ruszczyński, Shangzhe Yang","doi":"10.1137/23m1617965","DOIUrl":"https://doi.org/10.1137/23m1617965","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 3064-3087, September 2024. Abstract. We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and the decision variables. We call such problems conditional stochastic optimization problems. They arise in many applications, such as uplift modeling, reinforcement learning, and contextual optimization. We propose a specialized single time-scale stochastic method for nonconvex constrained conditional stochastic optimization problems with a Lipschitz smooth outer function and a generalized differentiable inner function. In the method, we approximate the inner conditional expectation with a rich parametric model whose mean squared error satisfies a stochastic version of a Łojasiewicz condition. The model is used by an inner learning algorithm. The main feature of our approach is that unbiased stochastic estimates of the directions used by the method can be generated with one observation from the joint distribution per iteration, which makes it applicable to real-time learning. The directions, however, are not gradients or subgradients of any overall objective function. We prove the convergence of the method with probability one, using the method of differential inclusions and a specially designed Lyapunov function, involving a stochastic generalization of the Bregman distance. Finally, a numerical illustration demonstrates the viability of our approach.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"40 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Minimal Extended Representations of Generalized Power Cones 论广义幂锥的最小扩展表示

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-10 DOI: 10.1137/23m1617205

Víctor Blanco, Miguel Martínez-Antón

引用次数: 0

Interpolation Conditions for Linear Operators and Applications to Performance Estimation Problems 线性算子的插值条件及其在性能估计问题中的应用

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-05 DOI: 10.1137/23m1575391

Nizar Bousselmi, Julien M. Hendrickx, François Glineur

{"title":"Interpolation Conditions for Linear Operators and Applications to Performance Estimation Problems","authors":"Nizar Bousselmi, Julien M. Hendrickx, François Glineur","doi":"10.1137/23m1575391","DOIUrl":"https://doi.org/10.1137/23m1575391","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 3033-3063, September 2024. Abstract. The performance estimation problem methodology makes it possible to determine the exact worst-case performance of an optimization method. In this work, we generalize this framework to first-order methods involving linear operators. This extension requires an explicit formulation of interpolation conditions for those linear operators. We consider the class of linear operators [math], where matrix [math] has bounded singular values, and the class of linear operators, where [math] is symmetric and has bounded eigenvalues. We describe interpolation conditions for these classes, i.e., necessary and sufficient conditions that, given a list of pairs [math], characterize the existence of a linear operator mapping [math] to [math] for all [math]. Using these conditions, we first identify the exact worst-case behavior of the gradient method applied to the composed objective [math], and observe that it always corresponds to [math] being a scaling operator. We then investigate the Chambolle–Pock method applied to [math], and improve the existing analysis to obtain a proof of the exact convergence rate of the primal-dual gap. In addition, we study how this method behaves on Lipschitz convex functions, and obtain a numerical convergence rate for the primal accuracy of the last iterate. We also show numerically that averaging iterates is beneficial in this setting.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"22 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Complexity-Optimal and Parameter-Free First-Order Methods for Finding Stationary Points of Composite Optimization Problems 寻找复合优化问题驻点的自洽最优和无参数一阶方法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-04 DOI: 10.1137/22m1498826

Weiwei Kong

{"title":"Complexity-Optimal and Parameter-Free First-Order Methods for Finding Stationary Points of Composite Optimization Problems","authors":"Weiwei Kong","doi":"10.1137/22m1498826","DOIUrl":"https://doi.org/10.1137/22m1498826","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 3005-3032, September 2024. Abstract. This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form [math], where [math] is a proper closed convex function, [math] is a differentiable function on the domain of [math], and [math] is Lipschitz continuous on the domain of [math]. The main advantage of this method is that it is “parameter-free” in the sense that it does not require knowledge of the Lipschitz constant of [math] or of any global topological properties of [math]. It is shown that the proposed method can obtain an [math]-approximate stationary point with iteration complexity bounds that are optimal, up to logarithmic terms over [math], in both the convex and nonconvex settings. Some discussion is also given about how the proposed method can be leveraged in other existing optimization frameworks, such as min-max smoothing and penalty frameworks for constrained programming, to create more specialized parameter-free methods. Finally, numerical experiments are presented to support the practical viability of the method.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"71 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Quadratically Convergent Sequential Programming Method for Second-Order Cone Programs Capable of Warm Starts 可实现热启动的二阶圆锥程序的二次收敛顺序编程法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-03 DOI: 10.1137/22m1507681

Xinyi Luo, Andreas Wächter

{"title":"A Quadratically Convergent Sequential Programming Method for Second-Order Cone Programs Capable of Warm Starts","authors":"Xinyi Luo, Andreas Wächter","doi":"10.1137/22m1507681","DOIUrl":"https://doi.org/10.1137/22m1507681","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2943-2972, September 2024. Abstract. We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities of active-set quadratic programming subproblem solvers and achieve a local quadratic rate of convergence. In order to overcome the nondifferentiability or singularity observed in nonlinear formulations of the conic constraints, the subproblems approximate the cones with polyhedral outer approximations that are refined throughout the iterations. For nondegenerate instances, the algorithm implicitly identifies the set of cones for which the optimal solution lies at the extreme points. As a consequence, the final steps are identical to regular sequential quadratic programming steps for a differentiable nonlinear optimization problem, yielding local quadratic convergence. We prove the global and local convergence guarantees of the method and present numerical experiments that confirm that the method can take advantage of good starting points and can achieve higher accuracy compared to a state-of-the-art interior point solver.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"76 3 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimality Conditions and Numerical Algorithms for a Class of Linearly Constrained Minimax Optimization Problems 一类线性约束最小优化问题的最优条件和数值算法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-03 DOI: 10.1137/22m1535243

Yu-Hong Dai, Jiani Wang, Liwei Zhang

引用次数: 0

Consensus-Based Optimization Methods Converge Globally 基于共识的优化方法全球趋同

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-03 DOI: 10.1137/22m1527805

Massimo Fornasier, Timo Klock, Konstantin Riedl

{"title":"Consensus-Based Optimization Methods Converge Globally","authors":"Massimo Fornasier, Timo Klock, Konstantin Riedl","doi":"10.1137/22m1527805","DOIUrl":"https://doi.org/10.1137/22m1527805","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2973-3004, September 2024. Abstract. In this paper we study consensus-based optimization (CBO), which is a multiagent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on an experimentally supported intuition that, on average, CBO performs a gradient descent of the squared Euclidean distance to the global minimizer, we devise a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions. The result unveils internal mechanisms of CBO that are responsible for the success of the method. In particular, we prove that CBO performs a convexification of a large class of optimization problems as the number of optimizing agents goes to infinity. Furthermore, we improve prior analyses by requiring mild assumptions about the initialization of the method and by covering objectives that are merely locally Lipschitz continuous. As a core component of this analysis, we establish a quantitative nonasymptotic Laplace principle, which may be of independent interest. From the result of CBO convergence in mean-field law, it becomes apparent that the hardness of any global optimization problem is necessarily encoded in the rate of the mean-field approximation, for which we provide a novel probabilistic quantitative estimate. The combination of these results allows us to obtain probabilistic global convergence guarantees of the numerical CBO method.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"317 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0